Graduation Year


Document Type




Degree Granting Department

Mechanical Engineering

Major Professor

Alex A. Volinsky, Ph.D.

Committee Member

Autar K. Kaw, Ph.D.

Committee Member

Nathan Crane, Ph.D.


residual stress, fracture, cracks interaction, Mo/Si multilayers, thermal distortions, curvature control, X-ray optics


Thin films and multilayers are widely used in many applications, ranging from X-ray optics to microelectronic devices. In service, the X-ray optics elements are exposed to the X-ray beam, which heats up the structure resulting in the thermal deformations, and consequently in distortions of the reflective surface. In addition, the excessive heating may activate interdiffusion in the multilayers coatings and result in degradation of their reflective performance and even film cracking. Therefore, analysis of the thermally-induced deformations and stresses in the X-ray optical elements is important.

The presented work is organized in two major parts. The first part examines formation of the peculiar periodic crack patterns observed in the thermally loaded Mo/Si multilayers. Film stress evolution during thermal cycling of the multilayers on Si substrate is analyzed. Results of the high-speed microscopic observations of crack propagation in the annealed Mo/Si multilayers are presented. The observations provide experimental evidence of the mechanism underlying formation of the periodic crack patterns.

In the second part, thermal deformations and the resulting surface curvature changes in the X-ray optics elements are analyzed. Finite element modeling is used to assess the potential to thermally control curvature in the X-ray mirrors consisting of the Mo/Si multilayers on a Si substrate. Influence of heating due to the X-ray beam irradiation on thermal deformations in the X-ray mirror bonded to a thick substrate is analyzed in-depth. The detailed consideration includes analysis of the thermal and structural mechanics simulations. Based on simulations of different model configurations, influence of structural composition on thermal distortions of the optics elements is addressed. Results of this analysis can be used to mitigate distortions of the X-ray optics caused by the X-ray beam and provide basis for further studies of thermally controlling surface curvature in the optical elements.